Methods, systems, and computer program products for modeling inductive effects in a circuit by combining a plurality of localized models

Abstract

Inductive effects in an integrated circuit device and/or system are modeled by partitioning the integrated circuit device and/or system into multiple windows or portions and determining a first localized inductance matrix for a first portion of the circuit and/or system and a second localized inductance matrix for a second portion of the circuit and/or system. The first and second localized inductance matrices are solved to obtain first and second localized susceptance vectors. The first and second localized susceptance vectors may be combined to form a susceptance matrix, which may be used directly in a susceptance-based simulator, or inverted to obtain a sparser inductance matrix that is representative of the inductive couplings in the entire integrated circuit device and/or system.

1 . A method of modeling inductive effects in an integrated circuit/system that comprises a plurality of conductors, the method comprising: 
 defining a plurality of windows, respective ones of the plurality of windows being associated with respective ones of the plurality of conductors and having other ones of the plurality of conductors contained therein; and    forming a plurality of localized susceptive coupling vectors, respective ones of the plurality of localized susceptive coupling vectors being populated with susceptive coupling elements by determining respective currents flowing through the other ones of the plurality of conductors such that the respective ones of the plurality of conductors associated with the respective ones of the plurality of windows have respective total magnetic fluxes of unity and the other ones of the plurality of conductors have respective total magnetic fluxes of zero;    combining the plurality of localized susceptive coupling vectors into a susceptance coupling matrix; and    transforming the susceptance coupling matrix so that the susceptance coupling matrix is symmetrical.    
   
   
       2 . The method of  claim 1 , wherein defining the plurality of windows comprises: 
 forming a localized inductance matrix for the respective ones of the plurality of conductors associated with the respective ones of the plurality of windows based on the respective other ones of the plurality of conductors contained in the respective ones of the plurality of windows.    
   
   
       3 - 5 . (Canceled)  
   
   
       6 . The method of  claim 1 , further comprising: 
 using the susceptance coupling matrix in a susceptance-based circuit simulator.    
   
   
       7 . The method of  claim 1 , further comprising: 
 inverting the susceptance coupling matrix to obtain an inductance coupling matrix.    
   
   
       8 . (Canceled)  
   
   
       9 . The method of  claim 7 , further comprising: 
 using the inductance coupling matrix in an inductance-based circuit simulator.    
   
   
       10 . The method of  claim 1 , wherein defining a plurality of windows comprises: 
 increasing respective sizes for respective ones of the plurality of windows so as to contain additional other ones of the plurality of conductors until susceptive coupling elements for the additional other ones of the plurality of conductors are less than a threshold.    
   
   
       11 - 18 . (Canceled)  
   
   
       19 . A system for modeling inductive effects in an integrated circuit/system that comprises a plurality of conductors, comprising: 
 means for defining a plurality of windows, respective ones of the plurality of windows being associated with respective ones of the plurality of conductors and having other ones of the plurality of conductors contained therein; and    means for forming a plurality of localized susceptive coupling vectors, respective ones of the susceptive coupling vectors being populated with susceptive coupling elements by determining respective currents flowing through the other ones of the plurality of conductors such that the respective ones of the plurality of conductors associated with the respective ones of the plurality of windows have respective total magnetic fluxes of unity and the other ones of the plurality of conductors have respective total magnetic fluxes of zero;    means for combining the plurality of localized susceptive coupling vectors into a susceptance coupling matrix; and    means for transforming the susceptance coupling matrix so that the susceptance coupling matrix is symmetrical.    
   
   
       20 . The system of  claim 19 , wherein the means for defining the plurality of windows comprises: 
 means for forming a localized inductance matrix for the respective ones of the plurality of conductors associated with the respective ones of the plurality of windows based on the respective other ones of the plurality of conductors contained in the respective ones of the plurality of windows.    
   
   
       21 - 23 . (Canceled)  
   
   
       24 . The system of  claim 19 , further comprising: 
 means for using the susceptance coupling matrix in a susceptance-based circuit simulator.    
   
   
       25 . (Canceled)  
   
   
       26 . The system of  claim 19 , further comprising: 
 means for sparsifying the inductance coupling matrix so as to cancel an inductive coupling element; and    means for adding a magnitude of the canceled inductive coupling element to respective diagonal elements in the inductance coupling matrix at rows and columns corresponding to ones of the plurality of conductors between which the the canceled inductive coupling element was determined.    
   
   
       27 . The system of  claim 19 , further comprising: 
 means for using the inductance coupling matrix in an inductance-based circuit simulator.    
   
   
       28 . The system of  claim 19 , wherein the means for defining a plurality of windows comprises: 
 means for increasing respective sizes for respective ones of the plurality of windows so as to contain additional other ones of the plurality of conductors until susceptive coupling elements for the additional other ones of the plurality of conductors are less than a threshold.    
   
   
       29 - 36 . (Canceled)  
   
   
       37 . A computer program product for modeling inductive effects in an integrated circuit/system that comprises a plurality of conductors, comprising: 
 a computer readable program medium having computer readable program code embodied therein, the computer readable program code comprising:    computer readable program code that is configured to define a plurality of windows, respective ones of the plurality of windows being associated with respective ones of the plurality of conductors and having other ones of the plurality of conductors contained therein; and    computer readable program code that is configured to form a plurality of localized susceptive coupling vectors, respective ones of the susceptive coupling vectors being populated with susceptive coupling elements by determining respective currents flowing through the other ones of the plurality of conductors such that the respective ones of the plurality of conductors associated with the respective ones of the plurality of windows have respective total magnetic fluxes of unity and the other ones of the plurality of conductors have respective total magnetic fluxes of zero;    computer readable program code configured to combine the plurality of localized susceptive coupling vectors into a susceptance coupling matrix; and    computer readable program code configured to transform the susceptance coupling matrix so that the susceptance coupling matrix is symmetrical.    
   
   
       38 . The computer program product of  claim 37 , wherein the computer readable program code that is configured to define the plurality of windows comprises: 
 computer readable program code that is configured to form a localized inductance matrix for the respective ones of the plurality of conductors associated with the respective ones of the plurality of windows based on the respective other ones of the plurality of conductors contained in the respective ones of the plurality of windows.    
   
   
       39 - 41 . (Canceled)  
   
   
       42 . The computer program product of  claim 37 , further comprising: 
 computer readable program code that is configured to use the susceptance coupling matrix in a susceptance-based circuit simulator.    
   
   
       43 . The computer program product of  claim 37 , further comprising: 
 computer readable program code that is configured to invert the susceptance coupling matrix to obtain an inductance coupling matrix.    
   
   
       44 . (Canceled)  
   
   
       45 . The computer program product of  claim 43 , further comprising: 
 computer readable program code that is configured to use the inductance coupling matrix in an inductance-based circuit simulator.    
   
   
       46 . The computer program product of  claim 37 , wherein the computer readable program code that is configured to define a plurality of windows comprises: 
 computer readable program code that is configured to increase respective sizes for respective ones of the plurality of windows so as to contain additional other ones of the plurality of conductors until susceptive coupling elements for the additional other ones of the plurality of conductors are less than a threshold.    
   
   
       47 - 54 . (Canceled)  
   
   
       55 . A computer program product, comprising: 
 a computer readable program medium having computer readable data structure embodied therein, the computer readable data structure comprising:    a symmetrical matrix that comprises a combination of susceptive coupling elements between conductors in an integrated circuit/system, the susceptive coupling elements being determined by defining a plurality of windows, respective ones of the plurality of windows being associated with respective ones of the conductors and having other ones of the conductors contained therein, and determining respective currents flowing through the other ones of the conductors such that the respective ones of the conductors associated with the respective ones of the plurality of windows have respective total magnetic fluxes of unity and the other ones of the conductors have respective total magnetic fluxes of zero.    
   
   
       56 - 60 . (Canceled)